Sampling with replacement.

Extended betabinomial posterior likelihood

Imagine a set of face down cards that on the other side are either red or white.

You only know the number of cards and you'd like to know how many are red. But it costs alot to turn over cards and you're willing to accept some uncertainty. Try playing with the tool below to see if it might help.

First set your prior parameters (use 0.5 for both if you're unsure and this with give the prior with least information)

And how many cards are there in total? (20 is a good number to try)

So you've turned over some cards. How many were red and how many white?

Number of red cards in sample:
Number of white cards in sample:

X-axis is a parameter, k

Y-axis is probability that the true number of red cards in the population, K, is less than or equal to k